# The Impossible Made Possible

Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."

In her Parade Magazine column of December 31, 1995, Marilyn states that it is impossible to spread 50 coins into 10 envelopes so that no two envelopes contain the same number of coins.

## An obvious alternative

James Thompson <Orkney@pe.net> and Zack Lau <zlau@arrl.org> both wrote to suggest that putting 14 coins into the ninth envelope and zero coins into the tenth envelope is one of many solutions to the problem. Personally, I don't believe that you've really spread the coins into ten envelopes if one of the envelopes contains zero coins, but I believe that alternative interpretations deserve consideration, so readers are free to reach their own conclusion.

## But wait -- there's more

In addition to his suggestion above, Zack also suggested cutting a coin in half. This would allow placing nine and one half coins into the ninth envelope, and four and one half coins into the tenth envelope.

## And now for something really creative

Mike Wermers <Mike128@aol.com> provided the most creative solution:

Marilyn's answer did not consider putting envelopes inside of envelopes. Putting an envelope (with coins) inside another envelope until all envelopes are contained inside of another envelope (except for the outer envelope(s)), several arrangements are possible such that each envelope contains a different number of coins (since envelopes that contain another envelope will "contain" the coins inside that envelope as well).

## Here's another way

Marcus Agatucci <maagatu@rs6000.cmp.ilstu.edu> suggests that the answer hinges on semantics: The question says only "that no two envelopes" contain the same number of coins, but it doesn't preclude the possiblity of more than two envelopes containing the same number of coins. Personally, I disagree with this interpretation, but I'll let the reader be the judge.
http://www.wiskit.com/marilyn/impossible.html last updated June 30, 1998 by herbw@wiskit.com